Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 6.9s

Alternatives: 12

Speedup: 1.0×

• 21.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + 6 \cdot \left(z \cdot \left(y - x\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* 6.0 (* z (- y x)))))

C

double code(double x, double y, double z) {
	return x + (6.0 * (z * (y - x)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (6.0d0 * (z * (y - x)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (6.0 * (z * (y - x)));
}

Python

def code(x, y, z):
	return x + (6.0 * (z * (y - x)))

Julia

function code(x, y, z)
	return Float64(x + Float64(6.0 * Float64(z * Float64(y - x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (6.0 * (z * (y - x)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Taylor expanded in z around 0 99.8%

   \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

3. Final simplification 99.8%

   \[\leadsto x + 6 \cdot \left(z \cdot \left(y - x\right)\right) \]

Alternative 2: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+60} \lor \neg \left(z \leq 6.4 \cdot 10^{+135}\right) \land z \leq 2.4 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z x))))
   (if (<= z -0.165)
     t_0
     (if (<= z 3e-24)
       x
       (if (or (<= z 2.8e+60) (and (not (<= z 6.4e+135)) (<= z 2.4e+226)))
         (* 6.0 (* z y))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double tmp;
	if (z <= -0.165) {
		tmp = t_0;
	} else if (z <= 3e-24) {
		tmp = x;
	} else if ((z <= 2.8e+60) || (!(z <= 6.4e+135) && (z <= 2.4e+226))) {
		tmp = 6.0 * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * x)
    if (z <= (-0.165d0)) then
        tmp = t_0
    else if (z <= 3d-24) then
        tmp = x
    else if ((z <= 2.8d+60) .or. (.not. (z <= 6.4d+135)) .and. (z <= 2.4d+226)) then
        tmp = 6.0d0 * (z * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * x);
	double tmp;
	if (z <= -0.165) {
		tmp = t_0;
	} else if (z <= 3e-24) {
		tmp = x;
	} else if ((z <= 2.8e+60) || (!(z <= 6.4e+135) && (z <= 2.4e+226))) {
		tmp = 6.0 * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * x)
	tmp = 0
	if z <= -0.165:
		tmp = t_0
	elif z <= 3e-24:
		tmp = x
	elif (z <= 2.8e+60) or (not (z <= 6.4e+135) and (z <= 2.4e+226)):
		tmp = 6.0 * (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * x))
	tmp = 0.0
	if (z <= -0.165)
		tmp = t_0;
	elseif (z <= 3e-24)
		tmp = x;
	elseif ((z <= 2.8e+60) || (!(z <= 6.4e+135) && (z <= 2.4e+226)))
		tmp = Float64(6.0 * Float64(z * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * x);
	tmp = 0.0;
	if (z <= -0.165)
		tmp = t_0;
	elseif (z <= 3e-24)
		tmp = x;
	elseif ((z <= 2.8e+60) || (~((z <= 6.4e+135)) && (z <= 2.4e+226)))
		tmp = 6.0 * (z * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.165], t$95$0, If[LessEqual[z, 3e-24], x, If[Or[LessEqual[z, 2.8e+60], And[N[Not[LessEqual[z, 6.4e+135]], $MachinePrecision], LessEqual[z, 2.4e+226]]], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008 or 2.8e60 < z < 6.3999999999999995e135 or 2.4e226 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around 0 64.9%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -0.165000000000000008 < z < 2.99999999999999995e-24

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 71.4%

      \[\leadsto \color{blue}{x} \]

   if 2.99999999999999995e-24 < z < 2.8e60 or 6.3999999999999995e135 < z < 2.4e226

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 97.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around inf 74.0%

      \[\leadsto 6 \cdot \color{blue}{\left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 74.0%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 74.0%

      \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+60} \lor \neg \left(z \leq 6.4 \cdot 10^{+135}\right) \land z \leq 2.4 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 3: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+60} \lor \neg \left(z \leq 4.6 \cdot 10^{+138}\right) \land z \leq 2.4 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* z (* x -6.0))
   (if (<= z 4.8e-24)
     x
     (if (or (<= z 2.2e+60) (and (not (<= z 4.6e+138)) (<= z 2.4e+226)))
       (* 6.0 (* z y))
       (* -6.0 (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * (x * -6.0);
	} else if (z <= 4.8e-24) {
		tmp = x;
	} else if ((z <= 2.2e+60) || (!(z <= 4.6e+138) && (z <= 2.4e+226))) {
		tmp = 6.0 * (z * y);
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 4.8d-24) then
        tmp = x
    else if ((z <= 2.2d+60) .or. (.not. (z <= 4.6d+138)) .and. (z <= 2.4d+226)) then
        tmp = 6.0d0 * (z * y)
    else
        tmp = (-6.0d0) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * (x * -6.0);
	} else if (z <= 4.8e-24) {
		tmp = x;
	} else if ((z <= 2.2e+60) || (!(z <= 4.6e+138) && (z <= 2.4e+226))) {
		tmp = 6.0 * (z * y);
	} else {
		tmp = -6.0 * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = z * (x * -6.0)
	elif z <= 4.8e-24:
		tmp = x
	elif (z <= 2.2e+60) or (not (z <= 4.6e+138) and (z <= 2.4e+226)):
		tmp = 6.0 * (z * y)
	else:
		tmp = -6.0 * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 4.8e-24)
		tmp = x;
	elseif ((z <= 2.2e+60) || (!(z <= 4.6e+138) && (z <= 2.4e+226)))
		tmp = Float64(6.0 * Float64(z * y));
	else
		tmp = Float64(-6.0 * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = z * (x * -6.0);
	elseif (z <= 4.8e-24)
		tmp = x;
	elseif ((z <= 2.2e+60) || (~((z <= 4.6e+138)) && (z <= 2.4e+226)))
		tmp = 6.0 * (z * y);
	else
		tmp = -6.0 * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-24], x, If[Or[LessEqual[z, 2.2e+60], And[N[Not[LessEqual[z, 4.6e+138]], $MachinePrecision], LessEqual[z, 2.4e+226]]], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 98.2%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 98.2%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 61.8%

      \[\leadsto z \cdot \color{blue}{\left(-6 \cdot x\right)} \]
   7. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot -6\right)} \]

   8. Simplified 61.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot -6\right)} \]

   if -0.165000000000000008 < z < 4.7999999999999996e-24

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 71.4%

      \[\leadsto \color{blue}{x} \]

   if 4.7999999999999996e-24 < z < 2.19999999999999996e60 or 4.60000000000000015e138 < z < 2.4e226

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 97.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around inf 74.0%

      \[\leadsto 6 \cdot \color{blue}{\left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 74.0%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 74.0%

      \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 2.19999999999999996e60 < z < 4.60000000000000015e138 or 2.4e226 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around 0 70.5%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+60} \lor \neg \left(z \leq 4.6 \cdot 10^{+138}\right) \land z \leq 2.4 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 4: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+136} \lor \neg \left(z \leq 2.9 \cdot 10^{+226}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* z (* x -6.0))
   (if (<= z 1.02e-23)
     x
     (if (<= z 3.8e+60)
       (* 6.0 (* z y))
       (if (or (<= z 7.4e+136) (not (<= z 2.9e+226)))
         (* -6.0 (* z x))
         (* z (* 6.0 y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.02e-23) {
		tmp = x;
	} else if (z <= 3.8e+60) {
		tmp = 6.0 * (z * y);
	} else if ((z <= 7.4e+136) || !(z <= 2.9e+226)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = z * (6.0 * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 1.02d-23) then
        tmp = x
    else if (z <= 3.8d+60) then
        tmp = 6.0d0 * (z * y)
    else if ((z <= 7.4d+136) .or. (.not. (z <= 2.9d+226))) then
        tmp = (-6.0d0) * (z * x)
    else
        tmp = z * (6.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.02e-23) {
		tmp = x;
	} else if (z <= 3.8e+60) {
		tmp = 6.0 * (z * y);
	} else if ((z <= 7.4e+136) || !(z <= 2.9e+226)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = z * (6.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = z * (x * -6.0)
	elif z <= 1.02e-23:
		tmp = x
	elif z <= 3.8e+60:
		tmp = 6.0 * (z * y)
	elif (z <= 7.4e+136) or not (z <= 2.9e+226):
		tmp = -6.0 * (z * x)
	else:
		tmp = z * (6.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 1.02e-23)
		tmp = x;
	elseif (z <= 3.8e+60)
		tmp = Float64(6.0 * Float64(z * y));
	elseif ((z <= 7.4e+136) || !(z <= 2.9e+226))
		tmp = Float64(-6.0 * Float64(z * x));
	else
		tmp = Float64(z * Float64(6.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = z * (x * -6.0);
	elseif (z <= 1.02e-23)
		tmp = x;
	elseif (z <= 3.8e+60)
		tmp = 6.0 * (z * y);
	elseif ((z <= 7.4e+136) || ~((z <= 2.9e+226)))
		tmp = -6.0 * (z * x);
	else
		tmp = z * (6.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-23], x, If[LessEqual[z, 3.8e+60], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.4e+136], N[Not[LessEqual[z, 2.9e+226]], $MachinePrecision]], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 98.2%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 98.2%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 61.8%

      \[\leadsto z \cdot \color{blue}{\left(-6 \cdot x\right)} \]
   7. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot -6\right)} \]

   8. Simplified 61.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot -6\right)} \]

   if -0.165000000000000008 < z < 1.02000000000000005e-23

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 71.4%

      \[\leadsto \color{blue}{x} \]

   if 1.02000000000000005e-23 < z < 3.80000000000000009e60

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 93.4%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around inf 79.3%

      \[\leadsto 6 \cdot \color{blue}{\left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 79.3%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 79.3%

      \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   if 3.80000000000000009e60 < z < 7.4000000000000002e136 or 2.89999999999999974e226 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around 0 70.5%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if 7.4000000000000002e136 < z < 2.89999999999999974e226

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around inf 70.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 70.8%

         \[\leadsto \color{blue}{\left(6 \cdot y\right) \cdot z} \]

   6. Simplified 70.8%

      \[\leadsto \color{blue}{\left(6 \cdot y\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+136} \lor \neg \left(z \leq 2.9 \cdot 10^{+226}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \end{array} \]

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-48} \lor \neg \left(z \leq 8 \cdot 10^{-24}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.2e-48) (not (<= z 8e-24))) (* 6.0 (* z (- y x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e-48) || !(z <= 8e-24)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.2d-48)) .or. (.not. (z <= 8d-24))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e-48) || !(z <= 8e-24)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.2e-48) or not (z <= 8e-24):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.2e-48) || !(z <= 8e-24))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.2e-48) || ~((z <= 8e-24)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.2e-48], N[Not[LessEqual[z, 8e-24]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000028e-48 or 7.99999999999999939e-24 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 96.3%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -8.20000000000000028e-48 < z < 7.99999999999999939e-24

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 73.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-48} \lor \neg \left(z \leq 8 \cdot 10^{-24}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.9e-35)
   (* 6.0 (* z (- y x)))
   (if (<= z 2.45e-23) x (* z (* 6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.9e-35) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 2.45e-23) {
		tmp = x;
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7.9d-35)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 2.45d-23) then
        tmp = x
    else
        tmp = z * (6.0d0 * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.9e-35) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 2.45e-23) {
		tmp = x;
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.9e-35:
		tmp = 6.0 * (z * (y - x))
	elif z <= 2.45e-23:
		tmp = x
	else:
		tmp = z * (6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.9e-35)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 2.45e-23)
		tmp = x;
	else
		tmp = Float64(z * Float64(6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.9e-35)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 2.45e-23)
		tmp = x;
	else
		tmp = z * (6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.9e-35], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-23], x, N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.89999999999999983e-35

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 94.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -7.89999999999999983e-35 < z < 2.4499999999999999e-23

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 73.4%

      \[\leadsto \color{blue}{x} \]

   if 2.4499999999999999e-23 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.3%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.3%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 98.4%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 98.4%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 98.4%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 7: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-45}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.2e-45)
   (* 6.0 (* z (- y x)))
   (if (<= z 1.25e-9) (* x (+ 1.0 (* z -6.0))) (* z (* 6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e-45) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 1.25e-9) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.2d-45)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 1.25d-9) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = z * (6.0d0 * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e-45) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 1.25e-9) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.2e-45:
		tmp = 6.0 * (z * (y - x))
	elif z <= 1.25e-9:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = z * (6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.2e-45)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 1.25e-9)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(z * Float64(6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.2e-45)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 1.25e-9)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = z * (6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.2e-45], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-9], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.1999999999999998e-45

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 94.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -8.1999999999999998e-45 < z < 1.25e-9

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf 73.0%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

   if 1.25e-9 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 99.7%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-45}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 3600000:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* 6.0 (* z (- y x)))
   (if (<= z 3600000.0) (+ x (* 6.0 (* z y))) (* z (* 6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 3600000.0) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 3600000.0d0) then
        tmp = x + (6.0d0 * (z * y))
    else
        tmp = z * (6.0d0 * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 3600000.0) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = 6.0 * (z * (y - x))
	elif z <= 3600000.0:
		tmp = x + (6.0 * (z * y))
	else:
		tmp = z * (6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 3600000.0)
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	else
		tmp = Float64(z * Float64(6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 3600000.0)
		tmp = x + (6.0 * (z * y));
	else
		tmp = z * (6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3600000.0], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.165000000000000008 < z < 3.6e6

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in y around inf 99.4%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]

   if 3.6e6 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 99.8%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 3600000:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.0045:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.16)
   (* 6.0 (* z (- y x)))
   (if (<= z 0.0045) (+ x (* y (* 6.0 z))) (* z (* 6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 0.0045) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.16d0)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 0.0045d0) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = z * (6.0d0 * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 0.0045) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * (6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.16:
		tmp = 6.0 * (z * (y - x))
	elif z <= 0.0045:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = z * (6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.16)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.0045)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(z * Float64(6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.16)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 0.0045)
		tmp = x + (y * (6.0 * z));
	else
		tmp = z * (6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.16], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0045], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.160000000000000003

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.160000000000000003 < z < 0.00449999999999999966

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Step-by-step derivation

      1. associate-*r* 99.9%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      3. flip-- 54.1%

         \[\leadsto x + \left(6 \cdot z\right) \cdot \color{blue}{\frac{y \cdot y - x \cdot x}{y + x}} \]

      4. associate-*r/ 52.8%

         \[\leadsto x + \color{blue}{\frac{\left(6 \cdot z\right) \cdot \left(y \cdot y - x \cdot x\right)}{y + x}} \]

   3. Applied egg-rr 52.8%

      \[\leadsto x + \color{blue}{\frac{\left(6 \cdot z\right) \cdot \left(y \cdot y - x \cdot x\right)}{y + x}} \]
   4. Step-by-step derivation

      1. associate-/l* 54.1%

         \[\leadsto x + \color{blue}{\frac{6 \cdot z}{\frac{y + x}{y \cdot y - x \cdot x}}} \]

      2. *-commutative 54.1%

         \[\leadsto x + \frac{\color{blue}{z \cdot 6}}{\frac{y + x}{y \cdot y - x \cdot x}} \]

      3. associate-/l* 54.1%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{\frac{y + x}{y \cdot y - x \cdot x}}{6}}} \]

      4. difference-of-squares 54.5%

         \[\leadsto x + \frac{z}{\frac{\frac{y + x}{\color{blue}{\left(y + x\right) \cdot \left(y - x\right)}}}{6}} \]

      5. associate-/r* 99.8%

         \[\leadsto x + \frac{z}{\frac{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}{6}} \]

      6. *-inverses 99.8%

         \[\leadsto x + \frac{z}{\frac{\frac{\color{blue}{1}}{y - x}}{6}} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{z}{\frac{\frac{1}{y - x}}{6}}} \]

   6. Taylor expanded in y around inf 99.4%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 99.4%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot z} \]

      2. *-commutative 99.4%

         \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]

      3. associate-*r* 99.5%

         \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]

   8. Simplified 99.5%

      \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]

   if 0.00449999999999999966 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. associate-*r* 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      3. *-commutative 99.7%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.0045:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 10: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 300000.0))) (* -6.0 (* z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 300000.0)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 300000.0d0))) then
        tmp = (-6.0d0) * (z * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 300000.0)) {
		tmp = -6.0 * (z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 300000.0):
		tmp = -6.0 * (z * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 300000.0))
		tmp = Float64(-6.0 * Float64(z * x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 300000.0)))
		tmp = -6.0 * (z * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 300000.0]], $MachinePrecision]], N[(-6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 3e5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right) + x} \]

   3. Taylor expanded in z around inf 99.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in y around 0 54.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -0.165000000000000008 < z < 3e5

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 69.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \left(6 \cdot \left(y - x\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* z (* 6.0 (- y x)))))

C

double code(double x, double y, double z) {
	return x + (z * (6.0 * (y - x)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z * (6.0d0 * (y - x)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (z * (6.0 * (y - x)));
}

Python

def code(x, y, z):
	return x + (z * (6.0 * (y - x)))

Julia

function code(x, y, z)
	return Float64(x + Float64(z * Float64(6.0 * Float64(y - x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (z * (6.0 * (y - x)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(z * N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Final simplification 99.8%

   \[\leadsto x + z \cdot \left(6 \cdot \left(y - x\right)\right) \]

Alternative 12: 35.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Taylor expanded in z around 0 36.4%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 36.4%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))